The 25-year-old’s current deal is set to expire in the summer, and he has started attracting interest from a host of top clubs at home and abroad, including Juventus and Napoli.
But the Premier League duo have been tracking D’Ambrosio for some time, and may attempt to make a cut price offer in January.
The player’s agent has revealed his client will not be signing a new contract at Torino, and refused to rule out the possibility of a move to Naples.
“I’ve read in the newspapers that we are working on his renewal, indeed that we are on the right road for that,” his agent Pisacane said.
“However, that is not right.
“A move to Napoli? I can’t exclude the possibility that Torino and Napoli have discussed a transfer because the agent is always the last to know.”
Sunderland boss Gus Poyet is particularly keen to strengthen in January, with his Sunderland side sitting in 19th place in the Premier League, currently three points from safety.
However Poyet has enjoyed an excellent start to his Sunderland career, winning three home games out of three in all competitions, including league triumphs over both Newcastle and Manchester City.